In circular machines for producing stockings or socks, one of the methods for closing the toe of the garment directly inside the machine that produces the latter is to start its formation with the toe itself, i.e. the foot, rather than with the cuff or upper edge; after the formation of a series of stitches to start the article, only an arc of needles, approximately corresponding to one half of the circumference of the cylinder, is employed to make the portion of fabric that will form the toe of the garment, after which the free edge of said portion of fabric is transferred to and over the needles of the opposite arc of needles corresponding to the remaining semicircle of the cylinder. This transfer may take place in two stages: in the known methods it is initiated in the first place by mechanical members that grip the fabric to be transferred and position it in such a way that, in the second stage, other mechanical members intervene on it to complete its transfer to the needles of the opposite arc, which proceed to "knit it into" the tubular portion of the article, the manufacture of which proceeds from this moment onward. However, this necessarily involves a not insignificant complexity of the mechanism necessary for carrying out the operations indicated above, and of the mechanical members of which this mechanism is composed.